Question

for what values of x is $x^2 + 2x = 24$ true?

• $-6$ and $-4$
• $-4$ and $6$
• $4$ and $-6$
• $6$ and $4$

Explanation:

Step1: Rearrange the equation

First, we need to set the equation to zero. Subtract 24 from both sides of the equation \(x^{2}+2x = 24\) to get \(x^{2}+2x - 24=0\).

Step2: Factor the quadratic equation

We need to find two numbers that multiply to -24 and add up to 2. The numbers are 6 and -4 because \(6\times(-4)=-24\) and \(6+(-4) = 2\). So we can factor the quadratic as \((x + 6)(x - 4)=0\).

Step3: Solve for x

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\). So we set each factor equal to zero:

• If \(x+6=0\), then \(x=-6\).
• If \(x - 4=0\), then \(x = 4\).

Answer:

4 and -6 (Option: 4 and -6)